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How do you solve #-5 > -5-3w#?

Answer 1

#w>0#

Right from the start, you can say that you need #w# to be positive because any negative value of #w# would make the product #(-3 * w)# positive, which in turn will make the right-hand side of the inequality bigger than #(-5)#.

SInce you need the left-hand side of the inequality to be strictly greater than the right-hand side, you cannot have #w=0#, since that would imply that

#-5 > -5 - 3 * 0#

#-5color(red)(cancel(color(black)(>)))-5#

So, the solution set for this inequality is #w>0#.

#-5 > -5 - 3w#

#-color(red)(cancel(color(black)(5))) + color(red)(cancel(color(black)(5))) > -3w#

#0 > -3w implies w > 0#

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Answer 2

Jameson Allen

To solve the inequality -5 > -5 - 3w, you need to isolate the variable w. First, simplify the inequality by combining like terms:

-5 > -5 - 3w

Next, add 5 to both sides to isolate the term involving w:

0 > -3w

Then, divide both sides by -3. Remember, when dividing or multiplying by a negative number, you need to flip the direction of the inequality sign:

0/(-3) < -3w/(-3)

0 < w

So, the solution to the inequality is w > 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #-5 &gt; -5-3w#?

How do you solve #-5 > -5-3w#?